Here we give a braid representation of each knot. These were taken from Gittings' paper, referenced below, which gives the minimum length braid in each case. In all cases except the knot 10136 this gives the number of strands also. For that knot we also give a braid with the minimum number of strands, taken from Jones' paper, as referred to by Gittings. For 11 crossing knots, when the braid length does not come from a minimal stranded braid, a minimal stranded braid is given, as provided to us by Alexander Stoimenow.
T. Gittings, Minimum Braids: A Complete Invariant of Knots and Links, Arxiv:math.GT/0401051
V. F. R. Jones, Hecke algebra representations for braid groups and link polynomials, Ann. of Math., 126 (1987) 335-388.
A. Stoimenow, Personal communication.